Building a satellite constellation may be a relatively expensive endeavor with costs at approximately $10,000 per pound. Depending on the number of satellites, deployment of certain satellite constellations may exceed capital outlays in the billions of dollars and yet the value they provide has justified the costs for those entities (e.g. nations, corporations, etc.) that have the resources required in the deployment of satellite constellations. Earth-orbiting satellite constellations serve many critical missions from delivering precise guidance and navigation to enhancing our understanding of climate change.
There is, however, a general interest in driving down the cost of satellite constellation deployment, so that a greater number of entities, such as nations, may participate in the benefits afforded by the use of satellite technology and so that the current entities exploiting satellite technology may exploit greater financial returns from their investments. Cost savings and return-on-investment (ROI) may be improved by a variety of mechanisms, including reducing the total number of satellites in the satellite constellation while achieving operational performance parameters (i.e. global coverage, revisit times, etc.), reducing the launch mass of the satellites at deployment of the satellite constellation, and increasing the operational lifetime of the satellite constellation while maintaining operation performance parameters.
For many missions, finding constellations that provide continuous coverage of the Earth using the fewest satellites is desirable. This problem has received a great deal of attention over the years, first with Easton (Easton, R. L. and Brescia, R., “Continuously Visible Satellite Constellations,” NRL Rept. 6896, Apr. 30, 1969), the contents of which are incorporated herein in its entirety, providing a six-satellite solution, followed by five-satellite designs by Walker (Walker, J. G., “Circular Orbit Patterns Providing Whole Earth Coverage,” Royal Aircraft Establishment, Tech. Rept. 70211, November 1970), the contents of which are incorporated herein in its entirety, and Ballard (Ballard, A. H., “Rosette Constellations of Earth Satellites,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES16, No. 5, September 1980, pp. 656, 665), the contents of which are incorporated herein in its entirety. By considering elliptical orbits, Draim (Draim, J. E., “Three- and Four-Satellite Continuous Coverage Constellations,” Journal of Guidance, Control, and Dynamics, Vol. 6, No. 6, 1985, pp. 725-730), the contents of which are incorporated herein in its entirety, discovered four-satellite configurations that provided continuous global coverage. Launch parameters may be specified for each of the aforementioned satellite constellation configurations. These launch parameters, as depicted in FIG. 1, may include semi-major axis (a), eccentricity (e), inclination (i), right ascension of ascending mode (a), argument of perigee (w), and mean anomaly (M).
Although Draim's initial configuration (i.e. launch parameters) provides continuous global coverage at initial deployment of the constellation, orbital perturbations, such as those shown in FIG. 2, may induce deviations from the original deployment configuration and degradation in operational performance parameters over the mission lifetime of the satellite constellation. Some of these orbital perturbations may include third-body effects of the sun and moon and the non-uniform mass distribution of the earth. To mitigate the degradation of the satellites in the satellite constellation, expensive station keeping (propellant expenditure=mass=cost) may be employed. Chao (Chao, C., Long-Term Orbit Perturbations of the Draim Four Satellite Constellations. AIAA Journal of Guidance, Control, and Dynamics, 1992. 15(6): p. 1406-1410), the contents of which are incorporated herein in its entirety, analyzed the long term perturbation effects on several Draim constellations over five and ten year periods, reporting coverage degradation of approximately 30% with no minimum elevation angle constraints and up to 60% at 10° minimum elevation angle. Counteracting the perturbations to maintain the Draim configuration through station keeping costs significant amounts of propellant.
Launch mass savings may be realized by reducing or eliminating propellant in the mass budget of the launch of a satellite constellation. In some cases, propellant used for station keeping may account for anywhere from 6% (Global Positioning System mission) to 50% (Clementine mission) of a satellite's total mass. Reducing or even eliminating the propellant required to perform a given mission may dramatically reduce the cost of a mission. The propellant costs are driven by a range of mission requirements which include station keeping, or maneuvers that provide the energy to counter undesired changes in the constellation design due to perturbing accelerations (e.g. oblate Earth, Sun, Moon, tides, relativity, etc.) to maintain predicted performance.